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How to calculate the number of possible connected simple graphs with $n . . . For Kn, there will be n vertices and (n (n-1)) 2 edges To determine how many subsets of edges a Kn graph will produce, consider the powerset as Brian M Scott stated in a previous comment If S is a finite set with n elements, then the powerset of S will have 2^n elements where n is the number of elements in the set S
Prove that if a graph has an Eulerian path, then the number of odd . . . Now, let's use these properties to prove the statement If a graph has an Eulerian path, there must be exactly two vertices with odd degrees (the starting and ending vertices) and all other vertices must have even degrees If the number of odd-degree vertices is 0, then all vertices have even degrees, which is fine
Graph theory: adjacency vs incident - Mathematics Stack Exchange Usually one speaks of adjacent vertices, but of incident edges Two vertices are called adjacent if they are connected by an edge Two edges are called incident, if they share a vertex Also, a vertex and an edge are called incident, if the vertex is one of the two vertices the edge connects
combinatorics - Every $k$ vertices in an $k$ - connected graph are . . . I have tried some ways - mainly using induction by removing one of the vertices of the set from the graph, and or using Menger's theorem to construct the cycle But I always encounter problems with making sure that the cycle I'm building deosn't have repeating edges etc Help would be greatly appreciated :) Thanks!
geometry - Orientation of a triangles vertices in 3D space: Clockwise . . . I would approach the issue from a completely different direction Consider a triangle in 3D with vertices at $\vec {v}_0$, $\vec {v}_1$, and $\vec {v}_2$ It has a directed normal $\vec {n}$, $$\vec {n} = \left (\vec {v}_1 - \vec {v}_0\right)\times\left (\vec {v}_2 - \vec {v}_0\right) \tag {1}\label {1}$$ If we look along $\vec {n}$ in one direction, the vertices are clockwise; in the opposite
Online tool for making graphs (vertices and edges)? Anyone know of an online tool available for making graphs (as in graph theory - consisting of edges and vertices)? I have about 36 vertices and even more edges that I wish to draw (why do I have so many?
How many nonisomorphic directed simple graphs are there with $n . . . A directed simple graph is a structure consisting of the set of vertices and a binary relation that is irreflexive For the case of the disconnected graph, the relation is empty, and there is one such structure up to isomorphism for each different number of vertices The Wikipedia pages on graph theory are a good source if you are struggling with an unclear textbook